Compact Second-Harmonic Generation in the C‑Exciton Band of 3R-MoS₂ for Integrated Quantum Photonics

We present a novel scheme for highly efficient second-harmonic generation in the visible spectrum using minimal volumes of 3R-phase molybdenum disulfide (MoS₂) integrated on a silicon nitride (Si₃N₄) ridge waveguide. The device is designed to operate near the C-exciton resonance of MoS₂, where the material exhibits its strongest second-order nonlinear response. A periodic array of nanometric MoS₂ stripes is patterned on the waveguide surface to form a one-dimensional photonic crystal, enabling strong field localization at the pump wavelength (λ_FF ≈ 890 nm) near the photonic band edge. This leads to resonant second-harmonic emission around 445 nm, close to the highly absorbing C-exciton. To mitigate the absorption while maintaining phase matching, we implement a counter-propagating pump configuration that ensures zero in-plane momentum mismatch and enables vertical out-coupling of the second harmonic signal via a leaky-mode resonance. The combination of strong nonlinear susceptibility, mode engineering, and resonant coupling allows for efficient frequency conversion within an interaction region only tens of nanometers thick, with an overall device footprint on the order of 1 μm². Full-wave 3D simulations predict conversion efficiencies up to 0.004% at peak pump intensities of 300 MW/cm². Moreover, the same architecture is compatible with spontaneous parametric down-conversion (SPDC), enabling integrated photon-pair generation with intrinsic modal and directional filtering. These features make the platform well-suited for compact, scalable nonlinear, and quantum photonic applications in the visible and near-infrared range.